CPM Homework Help : A2C Problem 13-107

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13-107.

Simplify each rational expression below.

$\large {\frac { \frac { x + 1 } { 2 x } } { \frac { x ^ { 2 } - 1 } { x } }}$
Step 1(a):
Multiply both the numerator and the denominator by a common denominator; use Giant Ones to eliminate the denominators.
$\frac{\frac{x+1}{2x}}{\frac{x^2-1}{x}}·\frac{2x}{2x}$
Step 2(a):
Factor the denominator and then simplify. (Look for another Giant One.)
$\frac{x+1}{2(x+1)(x-1)}$
Answer (a):
$\frac{1}{2(x-1)}$

$\large{\frac { \frac { 4 } { x + 3 } } { \frac { 1 } { x } + 3 }}$
Hint (b):
Follow the steps in part (a).
More Help (b):
A common denominator is $x\left(x + 3\right)$ .

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